I understood the riddle, and I must say that, if the prisioners cannot comunicate with each other after the whole thing starts, it is IMPOSSIBLE to solve this one. A lamp is like a bit, can hold only two informations at a time, 1 or 0. Since each prisioner can go to the room more than once, they cannot simply turn on the light if it's their second time on the room (by counting the nunber of days like DanielB stated, you would get the number of different prisioners who went to the room before him), if the following prisioner left the light on, the next one wouldn't know how many distinct prisoners have gone before, if he turns the light off, the next prisioner will think that only distinct prisoners have gone through.

So I can surely decrete: mathematically impossible, UNLESS the prisoners can comunicate with each other, or if the prisoners cannot go into the room more than once.